Open Access
2014 Lyapunov exponent and almost sure asymptotic stability of a stochastic SIRS model
Guoting Chen, Tiecheng Li, Changjian Liu
Publ. Mat. 58(S1): 153-165 (2014).


Epidemiological models with bilinear incidence rate usually have an asymptotically stable trivial equilibrium corresponding to the disease-free state, or an asymptotically stable nontrivial equilibrium (i.e. interior equilibrium) corresponding to the endemic state. In this paper, we consider an epidemiological model, which is a SIRS (susceptible-infected-removed-susceptible) model in uenced by random perturbations. We prove that the solutions of the system are positive for all positive initial conditions and that the solutions are global, that is, there is no finite explosion time. We present necessary and sufficient condition for the almost sure asymptotic stability of the steady state of the stochastic system.


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Guoting Chen. Tiecheng Li. Changjian Liu. "Lyapunov exponent and almost sure asymptotic stability of a stochastic SIRS model." Publ. Mat. 58 (S1) 153 - 165, 2014.


Published: 2014
First available in Project Euclid: 19 May 2014

zbMATH: 1329.92127
MathSciNet: MR3211831

Primary: 34D08 , 34F05 , 92D30

Keywords: SIRS model , stability , stochastic differential system

Rights: Copyright © 2014 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.58 • No. S1 • 2014
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